Question #43578

A vertical glass capillary tube of inner radius $r = 1.0 \text{ mm}$ is partially immersed in a liquid of refractive index $\mu = 1.5$. The liquid perfectly wets the glass (contact angle $\theta_0 = 0^\circ$). Due to gravity, the meniscus is not perfectly spherical; the exact height of the meniscus edge relative to its apex is measured to be $H = 1.2 \text{ mm}$. A broad, coherent parallel beam of monochromatic light of wavelength $\lambda = 600 \text{ nm}$ (in vacuum) is directed vertically upwards through the liquid column. Consider two specific rays from the incident beam: Ray 1 travels along the central axis and reflects at the meniscus apex. Ray 2 travels at a radial distance infinitesimally close to the glass wall ($x \to r$) and reflects at the extreme edge. Both rays start in phase from a common horizontal reference plane inside the liquid. What is the difference in their accumulated phase, $\Delta \Phi$, evaluated immediately after their respective reflections at the liquid-air interface?